Self-dual solutions to pseudo Yang–Mills equations

We study pseudo Yang–Mills fields on a compact 55-dimensional strictly pseudoconvex CR manifold MM i.e. critical points to the functional Y Mb(D)=12∫M‖ΠHRD‖2θ∧(dθ)2 on the space C(E,h)C(E,h) of all connections DD on a Hermitian vector bundle (E,h) over MM, such that Dh=0Dh=0. If A={D∈C(E,h):ξ⌋RD=0,Gθ∗(Tr(RD),dθ)=0} and D∈AD∈A is an absolute minimum to Y Mb:A→RY Mb:A→R then (i) ΔbTr(RD)=0 and (ii) DD is self-dual or anti-self-dual according to the sign of c2(θ,D)=∫Mθ∧{P2(D)−m−12mP1(D)∧P1(D)} [where Pk(D) is the kk-th Chern form of (E,D)(E,D)] and provided c2(θ,D)c2(θ,D) is constant on AA.